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Compared with microwave synthetic aperture radar (SAR), terahertz SAR (THz-SAR) is easier to achieve ultrahigh-resolution image due to its higher frequency and shorter wavelength. However, higher carrier frequency makes THz-SAR image quality very sensitive to high-frequency vibration error of motion platform. Therefore, this paper proposes a novel high-frequency vibration error estimation and compensation algorithm for THz-SAR imaging based on local fractional Fourier transform (LFrFT). Firstly, the high-frequency vibration error of the motion platform is modeled as a simple harmonic motion and THz-SAR echo signal received in each range pixel can be considered as a sinusoidal frequency modulation (SFM) signal. A novel algorithm for the parameter estimation of the SFM signal based on LFrFT is proposed. The instantaneous chirp rate of the SFM signal is estimated by determining the matched order of LFrFT in a sliding small-time window and the vibration acceleration is obtained. Hence, the vibration frequency can be estimated by the spectrum analysis of estimated vibration acceleration. With the estimated vibration acceleration and vibration frequency, the SFM signal is reconstructed. Then, the corresponding THz-SAR imaging algorithm is proposed to estimate and compensate the phase error caused by the high-frequency vibration error of the motion platform and realize high-frequency vibration error estimation and compensation for THz-SAR imaging. Finally, the effectiveness of the novel algorithm proposed in this paper is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]